my six year old son asked me how long it would take to travel across
our milky way (100,000 light years across)if we were able to travel a
(googooay to the googooway exponet miles per second. This number has
the equivalent of a one, with a hundered zeros after it , with an
exponet of a one with a hundered zeros after it. This speed is well
beyond Star Trek by a long shot. I am thinking of about an hour travel
perhaps? What do think the time frame would be?

Hi smartanswers,

Your guess is way high.  The speed you have specified is so huge that
the distance would be covered in an infinitesimal fraction of a
second.

I have not been able to find the terms "googooay" or "googooway" used
anywhere but in your question.  Ten to the hundredth power, equal to a
one with a hundred zeros after it, is commonly called a "googol."  A
"googolplex" is ten to the googolth power, but you have specified an
even bigger number, a googol to the googolth power.  I haven't found a
name for this number.  It would be a one followed by 100 googol zeros.

A light year is about 5,880,000,000,000 miles.  Throw in five more
zeros for the size of the Milky Way and you still have something on
the order of 10 to the 17th power.  This is an extremely tiny number
of miles in comparison to the number of miles your imaginary
spacecraft could travel in one second.

Using the ^ character to represent exponentiation, it would take about

1 / (10 ^ ( (100 googol) - 17 ) )

of a second to cross the galaxy.  In other words, you could cross the
galaxy almost 100 googol times in a second.


References

Wikipedia on "light year"
http://en.wikipedia.org/wiki/Light_year

Wikipedia on "googol"
http://en.wikipedia.org/wiki/Googol

Wikipedia on "googolplex"
http://en.wikipedia.org/wiki/Googolplex


If you need any further explanation of this, please ask for a clarification.

Regards,

--efn

---

Request for Answer Clarification by smartanswers-ga on 02 Aug 2005 17:47 PDT

So another words, this condition would in fact allow space travel thru
hundereds of galaxys in a very short period of time. What do you
sugest I tell my six year old a simple answer to his curious mind?

---

Clarification of Answer by efn-ga on 02 Aug 2005 18:26 PDT

First, racecar-ga is correct, I understated the number of times you
could cross the galaxy in a second.  It wouldn't be almost 100 googol,
it would be almost 10 to the 100-googolth power.

I'd suggest you tell your son first that scientists today don't think
anything can go faster than light, so the shortest time possible for
traveling 100,000 light years would be 100,000 years.

Second, the number you described, a googol to the googolth power, is
so huge that if it's a number of miles per second, it makes the size
of the galaxy extremely tiny in comparison.  Even if you changed the
speed units to inches per millennium and the distance to the estimated
size of the entire universe, the amount of time required for the trip
would be still be tiny.

I'm not sure I understand what you were getting at in your request for
clarification, so if this clarification doesn't help, please try again
to give me a more specific idea of what you are looking for, and I'll
try again to help.

--efn

---

Request for Answer Clarification by smartanswers-ga on 05 Aug 2005 17:45 PDT

Are we to asume that there is a boundry to our universe? If so--then
this rate of travel(assuming a person in a space craft was not pure
energy or light, and didn't crash into an asteroid etc.), would not be
practicle, nor safe. However, Is it possible to imagine this rate of
travel to discover other universes that simply are to far to
comprehend? Moreover, if proportionately comparing this rate of travel
to the measurment in size of one molecule of carbon, instead of say
the size of a human in a space craft, what would a googol to the
googolth power in this smaller proportional size take to travel across
our universe? Or is the size of particles irrelevant in this formular?

---

Clarification of Answer by efn-ga on 05 Aug 2005 20:06 PDT

> Are we to asume that there is a boundry to our universe?

For a discussion of this question, see:

http://answers.google.com/answers/threadview?id=460093

> However, Is it possible to imagine this rate of
travel to discover other universes that simply are to far to
comprehend?

I don't think imagining a high rate of speed equates to discovering
other universes.  However, it is certainly possible to imagine other
universes independently.

> Moreover, if proportionately comparing this rate of travel
to the measurment in size of one molecule of carbon, instead of say
the size of a human in a space craft, what would a googol to the
googolth power in this smaller proportional size take to travel across
our universe? Or is the size of particles irrelevant in this formular?

The size is irrelevant.  If you imagine a race between an elephant and
a mouse, if both go exactly two miles an hour, they will tie.  The
time is simply a function of the distance and the speed.

--efn

Ignoring the fact that you can't travel faster than light, and that
when you approach the speed of light you can no longer think of space
and time as independent entities, everything efn said looks right,
until the end, when (s)he says "In other words, you could cross the
galaxy almost 100 googol times in a second."  You could cross it far,
far more times than that.  100 googol is a 1 followed by 102 zeros. 
But as efn said, the speed is a 1 followed by 100 googol zeros.  Just
knock say 20 zeros off that number to be safe, so you still have way
more than 99 googol zeros after your 1, and that's how many times you
could cross the universe in a second.